Problem 4 - Chemistry Matter and Change

Question

Challenge The products of an acid-base reaction are \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{SO}_{4}^{2-}\) . Write a balanced equation for the reaction and identify the conjugate acid-base pairs.

Step-by-Step Solution

Answer

The balanced equation is \(\text{H}_2\text{SO}_4 + 2 \text{H}_2\text{O} \rightarrow 2 \text{H}_3\text{O}^+ + \text{SO}_4^{2-}\). Conjugate pairs: \(\text{H}_2\text{SO}_4/\text{HSO}_4^-\) and \(\text{H}_3\text{O}^+/\text{H}_2\text{O}\).

Step 1: Identify the Reaction Components

We are given the products of an acid-base reaction as \(\text{H}_3\text{O}^+\) and \(\text{SO}_4^{2-}\). To deduce the reactants, note that \(\text{H}_3\text{O}^+\) is typically formed from \(\text{H}_2\text{O}\) and an acid. \(\text{SO}_4^{2-}\) indicates a sulfate ion, which often comes from an acid like \(\text{H}_2\text{SO}_4\) that loses protons.

Step 2: Write the Unbalanced Equation

Assume sulfuric acid \(\text{H}_2\text{SO}_4\) reacts with water \(\text{H}_2\text{O}\) to produce \(\text{H}_3\text{O}^+\) and \(\text{SO}_4^{2-}\). The chemical equation for the reaction is \(\text{H}_2\text{SO}_4 + \text{H}_2\text{O} \rightarrow \text{H}_3\text{O}^+ + \text{SO}_4^{2-}\).

Step 3: Balance the Chemical Equation

Ensure the equation is balanced by checking the number of each type of atom on both sides. Starting with the reactants \(\text{H}_2\text{SO}_4 + \text{H}_2\text{O}\), we have 4 hydrogen (2 from sulfuric acid and 2 from water), 1 sulfur, and 5 oxygens initially. On the product side, \(\text{H}_3\text{O}^+\) and \(\text{SO}_4^{2-}\) have 3 hydrogen, 1 sulfur, and 5 oxygens. To balance hydrogen, add another \(\text{H}_2\text{O}\) as a starting reactant: \(\text{H}_2\text{SO}_4 + 2 \text{H}_2\text{O} \rightarrow 2 \text{H}_3\text{O}^+ + \text{SO}_4^{2-}\).

Step 4: Identify Conjugate Acid-Base Pairs

In the reaction, \(\text{H}_2\text{SO}_4\) donates a proton to \(\text{H}_2\text{O}\), forming \(\text{HSO}_4^-\) (which is the conjugate base of the acid \(\text{H}_2\text{SO}_4\)) and \(\text{H}_3\text{O}^+\) (the conjugate acid of the base \(\text{H}_2\text{O}\)). The conjugate acid-base pairs are: \(\text{H}_2\text{SO}_4/\text{HSO}_4^-\) and \(\text{H}_3\text{O}^+/\text{H}_2\text{O}\).

Key Concepts

Balanced Chemical Equation

A balanced chemical equation is crucial to think about in chemistry, especially during an acid-base reaction. It shows that matter is conserved, meaning the same number of each kind of atom appears on both sides of the equation.
In our sulfuric acid and water reaction, we must ensure that both atoms and charge are balanced. Initially, we write the unbalanced equation:
\[ \text{H}_2\text{SO}_4 + \text{H}_2\text{O} \rightarrow \text{H}_3\text{O}^+ + \text{SO}_4^{2-} \]
Here, we account for all the atoms - hydrogen, oxygen, and sulfur. Initially, you have four hydrogen atoms on the left (two from sulfuric acid and two from water) and five oxygen atoms. On the right, you have three hydrogens and five oxygens between the hydronium and sulfate ions.

• To balance the atoms, adjust the numbers of water molecules and hydronium ions.
• Once balanced, the equation reflects conservation of both mass and charge.

By doing this, our balanced equation becomes:
\[ \text{H}_2\text{SO}_4 + 2 \text{H}_2\text{O} \rightarrow 2 \text{H}_3\text{O}^+ + \text{SO}_4^{2-} \]
Now, hydrogen, sulfur, and oxygen are all balanced, ensuring a proper representation of the reaction.

Conjugate Acid-Base Pairs

Understanding conjugate acid-base pairs helps you identify how substances behave in a reaction. In any acid-base reaction, acids donate protons (H⁺), and bases accept them.
When an acid donates a proton, what remains is its conjugate base. Conversely, the base gains a proton to become its conjugate acid.

• In our example, sulfuric acid \(\text{H}_2\text{SO}_4\) donates a proton to water \(\text{H}_2\text{O}\).
• This forms the hydronium ion \(\text{H}_3\text{O}^+\) as the new conjugate acid.
• Meanwhile, \(\text{HSO}_4^-\) is the conjugate base formed from sulfuric acid without one proton.

This process forms two conjugate acid-base pairs:
\(\text{H}_2\text{SO}_4/\text{HSO}_4^-\) and \(\text{H}_3\text{O}^+/\text{H}_2\text{O}\).
Identifying these pairs allows you to predict product formation and understand proton dynamics in reactions.

Sulfuric Acid

Sulfuric acid, \(\text{H}_2\text{SO}_4\), plays a critical role as a strong acid in chemical reactions. It's known for its ability to donate protons quickly and completely, which usually makes it a complete dissociator in aqueous solutions.
It dissociates into ions:

• First, into \(\text{HSO}_4^-\) and \(\text{H}^+\) (proton), and then \(\text{HSO}_4^-\) can further lose a proton to form \(\text{SO}_4^{2-}\).

This dual-step dissociation partly explains its designation as a diprotic acid.Sulfuric acid is widely used in industry:

• In manufacturing fertilizers and in oil refinement.
• It is also important in car batteries due to its high reactivity.

As a strong acid, it serves as a benchmark in comparing strength of other acids in solution.

Hydronium Ion

The hydronium ion, represented as \(\text{H}_3\text{O}^+\), is a fundamental concept in understanding acid behavior in water. When an acid dissociates in water, it releases protons. These protons rapidly associate with water molecules to form \(\text{H}_3\text{O}^+\).
This interaction transforms the water into a stronger acid, the hydronium ion, which participates actively in involving other reactions.

• The hydronium ion is a crucial indicator of a solution's acidity.
• It is directly tied to the pH scale, which measures how acidic or basic a solution is, defined as the negative logarithm of hydronium ion concentration.

For example, when sulfuric acid is added to water, the free protons quickly create hydronium ions, consistent with the reaction's progression.Hydronium ions are key players in conducting electricity in aqueous solutions due to their charge and charge mobility.